Question

Answer in brief:
Derive the laws of reflection of light using Huygen's principle.

Answer 1

Law of Refraction using Huygens' Principle:
Similarly, we can use a Huygens construction to illustrate the law of refraction.
Here we must take into account a different speed of light in the upper and lower media. If the speed of light in a vacuum is $c$, we express the speed in the upper medium by the ratio $\frac{c}{n_i}$, where $n_i$ is the refractive index. Similarly, the speed of light in the lower medium is $\frac{c}{n_t}$. The points D, E and F on the incident wavefront arrive at points D, J and I of the plane interface XY at different times. In the absence of the refracting surface, the wavefront GI is formed at the instant ray DF reaches I. During the progress of ray CF from F to I in time $t$, however , the ray AD has entered the lower medium, where the speed in different. Thus if the distance $DG$ is $v_{i}t$, a wavelet of radius $v_{t}t$ is constructed with center at D. The radius $DM$ can also be expressed as
$DM=v_{i}t$
$=v_i\left(\frac{DG}{v_i}\right)$
$=\left(\frac{n_1}{n_t}\right)DG$
Similarly, a wavelet of radius $\frac{n_i}{n_t}$ JH is drawn centered at J. The new wavefront KI includes a point I on the interface and is tangent to the two wavelets at points M and N. The geometric relationship between the angles $i$ and $t$, formed by the representative incident ray AD and refracted ray DL, is Snell's law , which may be expressed as $n_i\sin {\theta }_i=n_i\sin {\theta }_i$.